Normal forms and embeddings for power-log transseries

Pavao Mardešić (1) , Maja Resman (2) , Jean-Philippe Rolin (1) , Vesna Županović (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 Department of Applied Mathematics [Zagreb]

Dulac series are asymptotic expansions of first return maps in a neighborhood of a hyperbolic polycycle. In this article, we consider two algebras of power-log transseries (generalized series) which extend the algebra of Dulac series. We give a formal normal form and prove a formal embedding theorem for transseries in these algebras.

Mots clés: Iteration theory; Dulac map; Normal forms; Embedding in a flow; Transseries

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]; Mathématiques [math]; Analyse classique [math.CA]

Pavao Mardešić, Maja Resman, Jean-Philippe Rolin, Vesna Županović. Normal forms and embeddings for power-log transseries. Advances in Mathematics, 2016, 303, pp.888 - 953. ⟨10.1016/j.aim.2016.08.030⟩. ⟨hal-01414966⟩